London (CNN) -- "The King's Speech" ruled Britain's BAFTA awards Sunday, with Colin Firth taking lead-actor honors for his role as the tongue-tied title character and co-stars Helena Bonham Carter and Geoffrey Rush claiming supporting-actor wins.

The film, which recounts World War II monarch George VI's struggle to overcome a stammer, won a total of seven trophies from the British Academy of Film and Television Arts, including best film, outstanding British film, best original screenplay and original music.

"I think I should thank the royal family, frankly, because they have done wonders for my career this year," said Bonham Carter, a winner on her fourth BAFTA nomination.

"I seem to be playing queens with ever-decreasing head sizes," said the actress, who also appeared in "Alice in Wonderland" with her head digitally enlarged. "Next year I will be the pin-headed queen."

And Firth -- who won his second award for best leading actor in two years -- told the audience, "I like coming here."

All three lead performers and the film itself are also nominated for Academy Awards, scheduled to be presented February 27 in Hollywood.

Natalie Portman took best leading actress for her performance as a tightly wound ballerina in "Black Swan," while best director went to David Fincher for "The Social Network," about the early days of the website Facebook. The award for best non-English film went to Swedish thriller "The Girl with the Dragon Tattoo."

Among other winners, "The Social Network" and its screenwriter, Aaron Sorkin, won a BAFTA for best adapted screenplay. The terrorism satire "Four Lions" won the award for best British debut, while "Toy Story 3" won best animated film.

Joel and Ethan Coen's reimagining of the 1969 Western "True Grit" won for best cinematography. And the mind-bending "Inception," about industrial spies who break into people's dreams, won for best visual effects.